Dept of Mathematics and Statistics
PhD in Mathematics, University of Maryland, College Park, 2001, Advisor: John J. Benedetto
MS in Applied Mathematics, University of Maryland, Baltimore County, 1997
BS in Mathematics, University of Maryland, Baltimore County, 1995
Primary: Applied harmonic analysis using Fourier series, wavelets, and frames. Secondary: Numerical analysis and algorithms, real and complex analysis, functional analysis, operator theory.
FOURIER SERIES
HARMONIC ANALYSIS
WAVELETS AND FRAMES
Refereed Book Chapters:
1. P.G. Casazza, M. Fickus, J. Kovacevic, M.T. Leon and J.C. Tremain, A Physical Interpretation of Tight Frames, in: Harmonic Analysis and Applications: In Honor of John J. Benedetto, C. Heil ed., Birkhauser, Boston, pp. 51-76 (2006).
Refereed Journal Articles:
2. J.J. Benedetto and M. Fickus, Finite normalized tight frames, Adv. Comput. Math., Vol. 18 (2003), pp. 357-385.
3. M. Fickus, B.D. Johnson, K. Kornelson and K. Okoudjou, Convolutional frames and the frame potential, Appl. Comput. Harmon. Anal., Vol. 19 (2005), pp. 77-91.
4. P.G. Casazza and M. Fickus, Fourier Transforms of Finite Chirps, EURASIP Journal on Applied Signal Processing, Vol. 2006 (2006), Article ID 70204, 7 pages.
5. M. Fickus and D.G. Mixon, Isotropic moments over integers lattices, Appl. Comput. Harmon. Anal., Vol. 26 (2009), pp. 77-96.
6. M. Fickus, Maximally equiangular frames and Gauss sums, J. Fourier Anal. Appl. 15 (2009) 413--427.
7. A. Chebira, M. Fickus and J. Kovacevic, Classifying compact convex sets with frames, Appl. Comput. Harmon. Anal. 27 (2009) 73-86.
8. P.G. Casazza and M. Fickus, Minimizing fusion frame potential, Acta Appl. Math. 107 (2009) 7-24.
9. G. Srinivasa, M. Fickus, Y. Guo, A. Linstedt and J. Kovacevic, Active mask segmentation of fluorescence microscope images, IEEE Trans. Image Process. 18 (2009) 1817-1829.
10. P.G. Casazza, M. Fickus, D. Mixon, Y. Wang and Z. Zhou, Constructing tight fusion frames, to appear in: Appl. Comput. Harmon. Anal., 14 pages.
11. M.L. Massar, M. Fickus, E. Bryan, D.T. Petkie and A.J. Terzuoli, Fast computation of spectral centroids, to appear in: Adv. Comput. Math., 12 pages.
Refereed Conference Proceedings:
12. P.G. Casazza, M. Fickus, J.C. Tremain and E. Weber, The Kadison-Singer Problem in mathematics and engineering, Proc. Gt. Plains Operator Theory Seminar, Contemp. Math. 414 (2006) 299-355.
13. G. Srinivasa, M. Fickus, M.N. Gonzalez-Rivero, S. Hsieh, Y. Guo, A. Linstedt, J. Kovacevic, Active mask segmentation for the cell-volume computation and Golgi-body segmentation of HeLa cell images, Proc. IEEE Int. Symp. Biomed. Imaging (2008) 348-351.
14. V. Oak, S. Garg, M. Fickus and J. Kovacevic, Voting-based active contour segmentation of fMRI images of the brain, Proc. IEEE Int. Conf. Image Process. (2008) 1100-1103.
15. P.G. Casazza, M. Fickus, Gradient descent of the frame potential, Proc. Sampl. Theory Appl. (2009), 4 pages.
16. A. Chebira, M. Fickus and M. Vetterli, Frame domain signal processing: framework and applications, to appear in: Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (2010)
17. D.C. Balcan, G. Srinivasa, M. Fickus and J. Kovacevic, Convergence behavior of the Active Mask algorithm, to appear in: Proc. IEEE Int. Conf. Acoust. Speech Signal Process. (2010)
18. R. Bhagavatula, M. Fickus, J.A. Ozolek, C.A. Castro and J. Kovacevic, Automatic identification and delineation of germ layer components in H&E stained images of teratomas, to appear in: Proc. IEEE Int. Symp. Biomed. Imaging (2010)
Non-Refereed Conference Proceedings Publications:
19. P.G. Casazza, M. Fickus, J. Kovacevi´c, M. Leon, and J.C. Tremain, Physical laws governing finite tight frames, Proc. SPIE, Wavelets X, M.A. Unser, A. Aldroubi and A.F. Laine, eds., Vol. 5207 (2003), pp. 371-380.
20. P.G. Casazza and M. Fickus, Chirps on finite cyclic groups, Proc. SPIE, Wavelets XI, M. Papadakis, A.F. Laine and M.A. Unser, eds., Vol. 5914 (2005), 6 pages.
21. M. Fickus, G.S. Seetharaman and M.E. Oxley, Multiscale moment transforms over the integer lattice, Proc. SPIE, Wavelets XII, D. Van De Ville, V.K. Goyal and M. Papadakis, eds., Vol. 6701 (2007), pp. 67011N/1-8.
22. G. Srinivasa, M. Fickus and J. Kovacevic, Active contour-based multiresolution transforms for the segmentation of fluorescence microscope images, Proc. SPIE, Wavelets XII, D. Van De Ville, V.K. Goyal and M. Papadakis, eds., Vol. 6701 (2007), pp. 67010I/1-15.
23. G. Srinivasa, M. Fickus and J. Kovacevic, Multiresolution multiscale active mask segmentation of fluorescence microscope images, Proc. SPIE. 7446 (2009) 744603/1-7.
24. P.G. Casazza, M. Fickus, D. Mixon, Y.Wang and Z. Zhou, Constructions and existence of tight fusion frames, Proc. SPIE. 7446 (2009) 744613/1-10.
Research Grants:
1. (2004-2007) "Applications of frames to internet coding, wireless communication, speech recognition and quantum information theory," National Science Foundation, Division of Mathematical Sciences, Program in Applied Mathematics, $56,762 (out of a total of $224,870).
2. (2006) "Image registration using polar wavelets," Air Force Office of Scientific Research, via the Air Force Research Laboratory, Information Directorate, $10,000 (out of a total of $200,000).
3. (2007-2008) "Time-frequency analysis of Doppler-shifted signals," Air Force Office of Scientific Research via the AFIT Research Support Fund, $27,677.
4. (2009) "Jitter estimation for directed energy weaponry," Air Force Research Laboratory, 711th Human Performance Wing, Human Effectiveness Directorate, $16,756.
5. (2009) "Functional analysis for passive navigation and surveillance," Air Force Office of Scientific Research, Physics and Electronics Directorate, Program on Sensing,
Surveillance, Navigation, $40,943.
6. (2009-2010) "Fusion frames for distributed processing and communication," Air Force Office of Scientific Research via the AFIT Research Support Fund, $24,959.